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Simplifying 5(3z + -1) + -3(z + 4) = 10(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 4) = 10(z + 1) (-1 * 5 + 3z * 5) + -3(z + 4) = 10(z + 1) (-5 + 15z) + -3(z + 4) = 10(z + 1) Reorder the terms: -5 + 15z + -3(4 + z) = 10(z + 1) -5 + 15z + (4 * -3 + z * -3) = 10(z + 1) -5 + 15z + (-12 + -3z) = 10(z + 1) Reorder the terms: -5 + -12 + 15z + -3z = 10(z + 1) Combine like terms: -5 + -12 = -17 -17 + 15z + -3z = 10(z + 1) Combine like terms: 15z + -3z = 12z -17 + 12z = 10(z + 1) Reorder the terms: -17 + 12z = 10(1 + z) -17 + 12z = (1 * 10 + z * 10) -17 + 12z = (10 + 10z) Solving -17 + 12z = 10 + 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. -17 + 12z + -10z = 10 + 10z + -10z Combine like terms: 12z + -10z = 2z -17 + 2z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -17 + 2z = 10 + 0 -17 + 2z = 10 Add '17' to each side of the equation. -17 + 17 + 2z = 10 + 17 Combine like terms: -17 + 17 = 0 0 + 2z = 10 + 17 2z = 10 + 17 Combine like terms: 10 + 17 = 27 2z = 27 Divide each side by '2'. z = 13.5 Simplifying z = 13.5
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